Topology Optimization of the Fiber-Reinforcement of No-Tension Masonry Walls

2017 ◽  
Vol 747 ◽  
pp. 36-43 ◽  
Author(s):  
Matteo Bruggi ◽  
Alberto Taliercio
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Fiber Reinforcement ◽  
Masonry Walls ◽  
Constrained Optimization Problem ◽  
Principal Stresses ◽  
Linear Elastic ◽  
Optimal Reinforcement ◽  
Optimization Formulation ◽  
Perfect Bonding

An innovative approach is proposed to define the optimal fiber-reinforcement of in-plane loaded masonry walls, modeled as linear elastic no-tension (NT) bodies. A topology optimization formulation is presented, which aims at distributing a prescribed amount of reinforcement over the wall, so as to minimize the overall elastic energy of the strengthened element. Perfect bonding is assumed at the wall-reinforcement interface. To account for the negligible tensile strength of brickwork, the material is replaced by an equivalent orthotropic material with negligible stiffness along the direction (s) undergoing tensile principal stress (es). Compressive principal stresses in the reinforcement are not allowed. A single constrained optimization problem allows both the equilibrium of the NT body to be enforced, and the optimal reinforcing layout to be spotted out, without any demanding incremental approach. Some preliminary numerical examples are shown to assess the capabilities of the proposed procedure and to identify the optimal reinforcement patterns for common types of masonry walls with openings.

Topology Optimization of Cellular Materials With Maximized Energy Absorption

2015 ◽  
Author(s):  
Josephine V. Carstensen ◽  
Reza Lotfi ◽  
James K. Guest ◽  
Wen Chen ◽  
Jan Schroers
Keyword(s):  
Topology Optimization ◽  
Mathematical Programming ◽  
Energy Absorption ◽  
High Performance ◽  
Optimization Problem ◽  
Cellular Materials ◽  
Component Level ◽  
Linear Elastic ◽  
Optimization Formulation ◽  
Level Scale

While topology optimization is typically employed for design at the component-level scale, it is increasingly being used to design the topology of high performance cellular materials. The design problem is posed as an optimization problem with governing unit cell and upscaling mechanics embedded in the formulation, and solved with formal mathematical programming. While design for linear elastic properties is generally well-established, this paper will discuss including nonlinear mechanics in the topology optimization formulation, also in the domain of cellular materials. In particular, the problem of maximizing total energy absorption of a cellular Bulk Metallic Glass material is considered and numerical and experimental analyses of the new design show that it has enhanced performance compared to conventional cellular topologies.

Cost Minimum Proportioning of Non-Slump Concrete Mix Using Genetic Algorithms

2012 ◽  
Vol 468-471 ◽  
pp. 50-54 ◽  
Author(s):  
Md. Moshiur Rahman ◽  
Mohd Zamin Jumaat
Keyword(s):  
Compressive Strength ◽  
Optimization Problem ◽  
Constrained Optimization Problem ◽  
Nonlinear Constrained Optimization ◽  
Constituent Material ◽  
Optimization Formulation ◽  
Materials Used ◽  
The Individual ◽  
The Cost ◽  
Optimal Quantity

This paper presents a generalized formulation for determining the optimal quantity of the materials used to produce Non-Slump Concrete with minimum possible cost. The proposed problem is formulated as a nonlinear constrained optimization problem. The proposed problem considers cost of the individual constituent material costs as well as the compressive strength and other requirement. The optimization formulation is employed to minimize the cost function of the system while constraining it to meet the compressive strength and workability requirement. The results demonstrate the efficiency of the proposed approach to reduce the cost as well as to satisfy the above requirement.

scholarly journals An Efficient Topology Description Function Method Based on Modified Sigmoid Function

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xingfa Yang ◽  
Jie Liu ◽  
Yin Yang ◽  
Qixiang Qing ◽  
Guilin Wen
Keyword(s):  
Topology Optimization ◽  
Function Method ◽  
Optimization Problem ◽  
Optimization Methods ◽  
Heaviside Function ◽  
Sigmoid Function ◽  
Topology Optimization Problem ◽  
Linear Elastic ◽  
Topology Description Function ◽  
Structural Compliance

Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

scholarly journals Nonconvex constrained optimization by a filtering branch and bound

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Kathrin Klamroth ◽  
Julia Niebling
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Constrained Optimization Problem ◽  
Numerical Tests ◽  
Nonconvex Constrained Optimization ◽  
Objective Value ◽  
Feasible Solutions ◽  
Quality Guarantee ◽  
Single Objective

AbstractA major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the $$\alpha $$ α BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective $$\alpha $$ α BB method fails, i.e., it terminates without ever finding a feasible solution.

Efficient Sensitivity Analysis for Multibody Dynamics Systems Using an Iterative Steps Method With Application in Topology Optimization

2011 ◽  
Author(s):  
Guang Dong ◽  
Zheng-Dong Ma ◽  
Gregory Hulbert ◽  
Noboru Kikuchi ◽  
Sudhakar Arepally ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Multibody Dynamics ◽  
Optimization Problem ◽  
Finite Difference Methods ◽  
Analysis Method ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Rotational Motions

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Topology Optimization for the Single Phase Flow Using Two Point Flux Approximation Model

2013 ◽  
Author(s):  
Guang Dong ◽  
Yulan Song
Keyword(s):  
Porous Media ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Approximation Model ◽  
Single Phase Flow ◽  
Topology Optimization Problem ◽  
Flux Approximation

The topology optimization method is extended to solve a single phase flow in porous media optimization problem based on the Two Point Flux Approximation model. In particular, this paper discusses both strong form and matrix form equations for the flow in porous media. The design variables and design objective are well defined for this topology optimization problem, which is based on the Solid Isotropic Material with Penalization approach. The optimization problem is solved by the Generalized Sequential Approximate Optimization algorithm iteratively. To show the effectiveness of the topology optimization in solving the single phase flow in porous media, the examples of two-dimensional grid cell TPFA model with impermeable regions as constrains are presented in the numerical example section.

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